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Smart Mater. Struct. 21 (2012) 025021 F Y Lee et al Figure 3. Energy density as a function of low electric field EL varying from 0.0 to 0.4 MV m−1. The high electric field was set as EH = 1.5 MV m−1 while the cold and hot source temperatures were maintainedatTcold =65◦CandThot =160◦C,respectively. the saturation polarization and relative permittivity varied nonlinearly as a function of electric field and the dielectric properties required in equation (4) were estimated from two piecewise regions of the isothermal bipolar D–E loops corresponding to the decreasing electric field branch. The electric displacement was assumed to depend linearly on the electric field in each region corresponding to electric field decreasing (i) from EH to Ecr(T) and (ii) from Ecr(T) to EL. 4.2. Effect of low electric field EL Figure 3 shows the average energy density harvested by sample 4 for five different Olsen cycles performed with low electric field EL equal to 0.0, 0.1, 0.2, 0.3 and 0.4 MV m−1. The high electric field was set as 1.5 MV m−1 while the cold and hot source temperatures were maintained at 65 and 160 ◦ C, respectively. The error bars correspond to two standard deviations or 95% confidence interval. The energy density reached a maximum at EL = 0.2 MV m−1. In fact, the electric displacement vanished during process 4–1 for EL set as 0.0 MV m−1 since this relaxor ferroelectric material possessed small remnant polarization at either temperatures used [58]. In other words, the sample was unable to retain its polarization at zero electric field. As a result, lowering the low electric field EL from 0.2 to 0.0 MV m−1 resulted in a reduction in the energy density from 192 to 172 J l−1/cycle. Meanwhile, raising the low electric field EL from 0.2 to 0.4 MV m−1 reduced the energy density from 192 to 187 J l−1/cycle, due to the reduced electric field span (EH − EL). Therefore, all measurements reported in the remainder of this study will correspond to EL = 0.2 MV m−1. 4.3. Sample variability Figure 4 shows the energy density as a function of high electric field EH between 0.4 and 1.5 MV m−1 collected from four different samples for temperatures Thot equal to (a) 100◦C, (b) 110◦C, (c) 120◦C and (d) 130◦C. The low electric field EL was 0.2 MV m−1 while the cold source temperature Tcold was maintained at 65 ◦C. The energy harvested represents the averaged values over five cycles performed under quasiequilibrium. Here also, the error bars represent a 95% confidence interval. Figure 4 indicates that sample variation was larger for low values of temperature Thot and electric field EH. In fact, the largest sample variation was found for Thot = 100◦C and EH = 0.4 MV m−1, with a maximum relative difference among samples of 19.7%. Meanwhile, sample variability was the lowest for Thot = 130 ◦C and EH = 1.5 MV m−1, with a maximum relative difference among samples of 9.1%. These results establish the consistency and repeatability of experimental measurements not only from one cycle to the next but also from one sample to the next. 4.4. Effect of cold source temperature Tcold Figures 5 and 6 show the average energy density harvested by sample 4 as a function of high electric field EH ranging from 0.4 to 2.5 MV m−1 for cold source temperature Tcold equal to 65 and 45 ◦C, respectively. Here also, the hot source temperature Thot was equal to (a) 100 ◦C, (b) 120 ◦C, (c) 130 ◦C and (d) 160◦C. The low electric field was set as EL = 0.2 MV m−1. Figures 5 and 6 establish that the energy density ND increased as the cold source temperature Tcold decreased. For example, for the conditions EH = 2.5 MV m−1 and Thot = 160 ◦C, the energy density increased from 343 to 442 J l−1/cycle, or by 29% when Tcold was reduced from 65 to 45◦C. Indeed, this was attributed to the increase in electric displacement span [D(E, Tcold)−D(E, Thot)]. In other words, more free charges were collected at the electrode surface as Tcold was lowered. However, reducing Tcold from 65 to 45◦C increased the cycle period from 51.9 to 124 s and in turn decreased the corresponding power density from 6.61 to 3.56 W l−1. This reduction in power density was attributed to an increase in the time required for isoelectric cooling (process 4–1) to be performed under quasiequilibrium conditions. This may be a consequence of the slow dielectric relaxation of PLZT in the ergodic relaxor phase at Tcold [58]. The dipole reorientation contributing to the polarization change slows down at low temperatures due to the increasing energy barrier necessary to activate and reorient the polar nanodomains [59]. 4.5. Effect of hot source temperature Thot Figures 5 and 6 also establish that the energy density increased as the hot source temperature Thot was raised from 100 to 160◦C for a given high electric field EH. Between Tcold and Thot ≥ TCurie, the 8/65/35 PLZT samples underwent a phase transition from ferroelectric (polar) to ergodic relaxor (non-polar). In fact, the largest energy density was obtained at Thot near the ferroelectric–ergodic-relaxor phase transition temperatures TCurie ≤ 160 ◦C. However, increasing the operating temperature difference (Thot −Tcold) in excess of 135 ◦C resulted in large thermal stresses, causing the sample to crack. 5PDF Image | Pyroelectric waste heat harvesting using relaxor ferroelectric
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